A privileged supply system is known from document U.S. Pat. No. 6,857,272. This privileged supply system operates on the basis of predetermined operating ranges depending on the flow rate of the fuel, in which privileged injection is either enabled or not.
However, such a system has the drawback of being enabled even for operating conditions for which this is not necessary. Indeed, there exist steady state operating conditions with a low fuel flow rate which do not have any risk of extinction, wherein the privileged supply is enabled even when this is not necessary. In this case, a hot trail forms, which may in certain extreme cases ovalize the turbine rings.